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2019
Fourth-Grade Teachers Use of MTSS-RTI to Teach
Mathematical Word Problem-Solving
Theodell Joanna Blake
Walden University
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Walden University
College of Education
This is to certify that the doctoral dissertation by
Theodell J. Blake
has been found to be complete and satisfactory in all respects, and that any and all revisions required by
the review committee have been made.
Review Committee
Dr. Barry Birnbaum, Committee Chairperson, Education Faculty Dr. Asoka Jayasena, Committee Member, Education Faculty
Dr. Narjis Hyder, University Reviewer, Education Faculty
Chief Academic Officer Eric Riedel, Ph.D.
Walden University 2019
Abstract
Fourth-Grade Teachers Use of MTSS-RTI to Teach Mathematical Word Problem-Solving
by
Theodell J. Blake
MS, Touro College, 2007 Med, University of Sheffield, 1998
BS, Andrews University, 1992
Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy Special Education
Walden University May 2019
Abstract
Schools in Florida used the multitiered system of support response to intervention framework to help students achieve the state and national standards but, in the national report card, 61% of the fourth-graders assessed in mathematics failed to achieve proficiency. Research indicated that the students lacked mathematical word problem-solving skills. The purpose of the qualitative study was to discover how fourth-grade special and general education teachers used the response to intervention framework evidence-based curriculum, instruction, intervention, assessment, and student data to teach math word problem-solving skills to children who have persistent and significant difficulties. Welner’s zone of mediation framework and Vygotsky’s sociocultural theory form the conceptual framework for the study. The teachers provided data through in-depth interviews, math intervention program, training document, teachers’ guides, assessment tools, and observation. All the data was uploaded to the latest version of NVivo and analyzed based on the research questions. The study findings showed that participants used all the features of the response to intervention framework to teach math word problem-solving skills and address the needs of at-risk students. Teachers should continuously reinforce math vocabulary, terminology, and math reading comprehension skills of students. Administrators and teachers should be able to use the findings of this study to improve the use of the response to intervention features to develop the math word problem-solving skills of students and influence teachers’ pedagogical practices.
Fourth-Grade Teachers Use of MTSS-RTI to Teach Mathematical Word Problem-Solving
by
Theodell J. Blake
MS, Touro College, 2007 Med, University of Sheffield, 1998
BS, Andrews University, 1992
Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy Special Education
Walden University May 2019
Dedication
I dedicate my doctoral study to my children Gerard Frederick, Denis Frederick, Blair Frederick, Diana Frederick, and Colette Elwin-Frederick for their encouragement and support. I dedicate my study to my grandchildren Menelyk Frederick, Sarabi Frederick, and Caelen Frederick as an example to show that they can achieve the goals they set for themselves. I dedicate study to my deceased Mother may she rest in peace, Dr. Joyce Barry-Hogan for her inspiration. I dedicate it to my deceased husband, Lenford Blake may he rest in peace, for his financial and physical support during the doctoral journey. I dedicate my study to my sister Sharon St Clair for her support and encouragement. Thank you for being there when I needed a push.
Acknowledgments
My sincere thanks and gratitude to my first mentor and second committee chairperson, the inspiring and amazing Dr. Barry Birnbaum for his patience, feedback, and guidance through these eight years. My sincerest thanks to Dr. Sheri Anderson who was my second mentor and my first chairperson who took me through the KAMs and Dissertation Prospectus. My sincerest thanks and gratitude to my methodologist, Dr. Asoka Jayasena for her inputs, immediate feedbacks, patience, and guidance throughout the dissertation process to help me achieve my goals. Thanks to Dr. Paula Dawidowicz for her efforts to ensure that I have a working committee during the difficult early stages of the process. Thanks to the different URR official and Dr. Narjis Hyder for their support and inputs. Thanks to the principal and participating teachers whose inputs, and participation that made this research study possible. I appreciate the new friendships formed during this process.
i Table of Contents List of Tables ...v Chapter 1 ...1 Introduction ...1 Background .. ...4
Multitiered Response to Intervention ... 11
Problem Statement ...13
Purpose of the study ...16
Research Question ...17
Conceptual and Theoretical Framework ...18
Nature of the Study ...20
Definitions...23
Assumptions ...25
Scope and Delinitations ...26
Limitations ...27 Significance...28 Social Change ... 28 Summary ...29 Chapter 2: ……….……….32 Introduction ...32
Literature Search Strategy...38
ii
Conceptual Framework . ...41
Mathematics Word Problem-Solving Instruction ...43
Math Word Problem-Solving Difficulties ... 46
The Response to Intervention Model Services Delivery System...49
Implementing the Response to Intervention Model ... 56
Response to Intervention and Math Teaching Strategies ... 61
Roles and Responsibilities of Educators ... 66
Co-teaching and Response to Intervention Practices ... 69
Professional Development ... 71
Challenges and Benefits of Response to Intervention Implementation ... 76
The Gap in the Literature ...78
Summary and Conclusion ...80
Chapter 3.. ...83
Introduction ...83
Research Design and Rationale ...84
Role of the Researcher ...87
Methodology: Research Site ...89
Instrumentation ... 92
Data Analysis Plan ... 95
Issues of Trustworthiness ...96
Ethical Procedures ... 97
iii Chapter 4.. ...100 Introduction ...100 Setting……….101 Demographics ...103 Data collection ...104 Data Analysis ...106 Evidence of Trustworthiness...107 Results. ...108
Response to Intervention Tier One ...109
Characterisitics of Students with Math Difficulties ... 110
Response to intervention Tier Two Intervention ... 112
Progress Monitoring... 113
Intervention Program ... 114
Teaching Strategies ...115
Observation of A Tier two Intervention Lesson ...118
Math Program ... 114
Florida Standards Assessments Failure ... 114
Planning and Preparation ...122
Co-teaching ...122
Professional Development Activities ...123
Support System and Coaching ... 125
iv
Response to Intervention Improvement ... 126
Challenges and Barriers ... 126
Summary ...128
Chapter 5 ...132
Introduction ...132
Interpretation of the Findings...135
Limitation of the Study ...143
Recommendations ...144
Implications...144
Conclusion ...145
References ...147
Appendix A: Teacher Interview Protocol ...168
Appendix B: Checklist to Evaluate Teacher’s Lesson Plan ...171
Appendix C: Blank Tier One and Two Critical components Checklist...172
v List of Tables
Table 1: Fourth-graders Performance on 2018 State Assessment……….14
Table 2: Demographics Details of Research Setting..………...89
Table 3: Demographics Details of Research Setting………...101
Table 4: Fourth-Grade Teachers' Subject Assignments………..102
Table 5: The Work Demographics of Participants ……….103
Chapter 1
Introduction
Mathematics is a logical, hierarchical, collection of interconnected concepts and competencies. It involves the development of computation skills, conceptual
understanding of numbers, their relationships, combinations, operations, reasoning, and word problem-solving skills (Bryant et al., 2014). Many fourth-grade students are having difficulties developing mathematical proficiency and word problem-solving skills
because of deficits in computation fluency and reading comprehension skills.
Comprehension skills are essential to understanding the elements of mathematics (math) word problems (Bjorn, Aunola, & Nurmi, 2016). Through math word problem-solving, learners apply fundamental knowledge, concepts, and skills to real-world situations (Swanson, Lussier, & Orosco, 2015). Word problem-solving is critical to determine mathematics proficiency, as evident in the national assessment (Krawec, 2014; Krawec & Huang, 2016). According to the National Assessment of Education Progress [NAEP], (2015) National Report Card, an overall 40% of fourth-graders achieved math
proficiency. The National Report Card also indicated that in the state of Florida 39% of fourth-graders achieved math proficiency. Developing mathematics word problem-solving skills are essential to students’ progress in elementary, middle school, high school, college, and acquiring life skills (Nurlu, 2015). Students must be able to purchase items and services that require applying mathematics concepts and procedures using word problem-solving skills (Nurlu, 2015).
Word problem-solving is an essential skill for college preparation as evident in the Common Core State Standards for Mathematics [CCSS-M] (Krawec, 2014; Krawec & Huang, 2016). The focus of CCSS-M is students’ learning of mathematical thinking, reasoning, conceptual understanding, and word problem-solving (Jitendra, 2013). Of the eight M, six are explicitly linked to word problem-solving. Moreover, the CCSS-M require students’ engagement in understanding and applying mathematics knowledge and skills in school and society (Kingsdorf & Krawec, 2014). The reauthorized Individual with Disabilities Education Act (IDEA) of 2006 and The Every Student Succeeds Act (ESSA), of 2015, do not explicitly mandated that the States use the multi-tiered response to intervention model to provide students with early intervening services. However, many students do not acquire the skills taught to them in the general education classroom through the CCSS-M core instruction (Kingsdorf & Krawec, 2014).
The Individual with Disabilities Education Act (IDEA) of 2006, regulation 34CFR 300.307, (c) mandated that the States “must permit the use of a process based on the child’s response to scientific, research-based intervention” to determine that a struggling student has a specific learning disability (p.11). The reauthorized Elementary and Secondary Education Act of 1965 cited as ESSA (2015) mandated the use of whole school programs to address the needs of students at-risk of not meeting state academic standards. Included in the strategies recommended for addressing the needs of struggling students are the “implementation of a schoolwide tiered model and early intervening services, coordinated with similar activities and services carried out under IDEA, 20 U.S.C. 1400 et seq” (p. 65). The United States Department of Education [USDOE]
(2007) guidance for early intervention services, evidence-based interventions and the provision of special education services for students with learning disabilities. The USDOE explained that the States criteria permit the use of the multi-tiered response to intervention model in addition to other assessment tools and strategies to provide early intervening services to determine that a struggling student has a disability and not at-risk for failure because of inadequate instruction.
Musgrove, Director of the Office of Special Education Programs in 2011, defined the response to intervention model as a multi-tiered instructional framework. It is a three-tiered school-wide approach used to address the needs of all students, including
struggling learners and students with disabilities. According to the USDOE (2007), in tier one (Primary intervention) all students in the general education classroom receive high-quality scientific research-based instruction. In tier two (Secondary intervention) small groups of students who are at-risk for academic failure receive specialized instruction. In tier three (Tertiary intervention) students with intensive needs receive specialized, individualized instruction. The USDOE recommended that all students participate in the schoolwide multi-tiered response to intervention model. The multi-tiered response to intervention model components are
• all students receive high-quality scientific research-based instruction; • continuous monitoring of their progress;
• screening of all students for academic and behavioral problems;
• also, multi-tiered levels of instruction and intervention in the general education
Background
In 2006, the Florida Department of Education (FDOE) partnered with the University of South Florida to facilitate and implement a multi-tiered response to intervention model in the state. The mission of the project was to provide support, technical assistance and training across Florida on the multi-tiered response to
intervention model; and systematically assess the impact of the multi-tiered response to intervention model implementation in 34 pilot schools in seven demonstration school districts across the state during 2007 to 2010. The statewide training element provides school-based teams and teachers with the knowledge and skills necessary to implement the multi-tiered response to intervention model (Stockslager, Castillo, Hines, & Curtis, 2013). In 2008, the Florida Department of Education published a Response to
Instruction/Intervention (RTI) Implementation Plan. The plan was the preliminary, official state-level framework to assist districts with the essential components,
definitions, and applications to develop and support schoolwide multi-tiered response to intervention model implementation. The goal of the plan was to integrate data-based problem-solving and the multi-tiered response to intervention system with various elements of Florida’s education system to create a multi-tiered system of support. FDOE adopted the multi-tiered system of support-response to intervention (MTSS-RTI) model in response to the reauthorized Elementary and Secondary Education Act of 1965, cited then as No Child Left Behind Act (NCLB) of 2002 and Individual with Disabilities Education Act (2004). According to Stockslager et al. (2013), the No Child Left Behind Act included the use of scientific research-based curriculum, data-based decision making,
and evidence-based practices to increase students’ performance on the statewide assessment.
The MTSS-RTI model is described as a comprehensive, integrated approach to address the behavioral, academic and social-emotional needs of all students (Stockslager et al., 2013). Throughout the state of Florida, Trained specialists provided technical assistance and training on data-based problem-solving within a multi-tiered system in schools. These specialists collaborated with other content specialists (e.g., math and reading) to provide internal professional development to improve teachers’ pedagogical practices (Florida Department of Education, 2017). In addition to addressing students’ academic needs, the MTSS-RTI model included instruments to assist schools in using the available resources more efficiently (Castillo et al., 2016). The purpose of this qualitative single-case study was to discover how fourth-grade special and general education
teachers used the MTSS-RTI model evidence-based curriculum, instruction, intervention, assessment, and student data to teach math word problem-solving skills.
The MTSS-RTI framework incorporates a combination of whole-class scientific research-based instruction and additional small-group and individual intervention (Griffin, League, Griffin, & Bae, 2013; Hunt & Little, 2014; Powell et al., 2015). The aim is to ensure that every child has access to scientific research-based curricula based on the common core state standards and instruction regardless of their cultural and linguistic backgrounds, abilities, or disabilities. The MTSS-RTI model is a practical system for teachers to use to address the academic needs of each child in the general education setting.
According to Cavendish, Harry, Menda, Espinosa, and Mahotiere (2016), there is limited literature on classroom teachers’ implementation of the MTSS-RTI model in the natural school environment. Teachers face many challenges in teaching students from diverse cultural and linguistic backgrounds, with different abilities and disabilities, and behavior issues. Tyler (2016) posited that teachers must reevaluate their misconceptions and negative perceptions of racial, linguistic and socioeconomic diversity in the school environment. Therefore, general and special education teachers with different knowledge and expertise work collaboratively to design instruction, co-teach and evaluate student outcomes. General and special education teachers used co-teaching with the MTSS-RTI strategies to help the students accessed and progress through the general education curriculum. General education teachers are responsible for instruction and work
collaboratively with special education teachers to address the needs of struggling students from diverse cultural and linguistic backgrounds, with and without disabilities. Special education teachers provide explicit, intensive instruction for, small homogeneous groups and individual students struggling with academic skills (Meyer & Behar-Horenstein, 2015).
Cavendish et al. (2016) listed teachers’ requirement to implement the MTSS-RTI framework, using the CCSS-M and solving the problems that occur in the classroom daily. To successfully implement the MTSS-RTI methods and standards teachers must understand the MTSS-RTI purpose, be knowledgeable about math content and the
standards and believe in their students’ ability to be successful. Teachers must participate in long-term intensive professional development opportunities, so they can be prepared to
use appropriate instruction, intervention, and assessment and analyze and interpret
students’ results. Additionally, they should have adequate resources to encourage them to utilize the MTSS-RTI framework to support student learning. It was necessary to
discover if these MTSS-RTI features are available in the targeted school for fourth-grade teachers to successfully address the needs of students struggling with mathematics word problem-solving.
Research on teaching solving word problems is limited to early elementary, middle school and high school classes. Most research focused on word problem-solving in Kindergarten through grade three or five (De Knock & Harskamp, 2014), or the middle and high school grades (Doabler & Fien, 2013; Krawec & Hauang, 2016). The
researchers (De Knock & Harskamp, 2014; Doabler & Fien, 2013; Krawec & Hauang, 2016) used research teams instead of classroom teachers to provide intervention to students during their investigations of mathematics intervention effectiveness. They provided support for interventionists who implemented intervention and the monitored students’ progress for making instructional decisions (Jitendra, 2013). Other research focused on instructional strategies utilized during the intervention for Kindergarten through grade three or five (De Knock & Harskamp, 2014). They also focused on middle and high school grades (Doabler & Fien, 2013; Jitendra et al., 2015; Krawec & Huang, 2016; Orosco, 2013). The lack of research on teachers’ use of MTSS-RTI practices to develop fourth-graders mathematics word problem-solving skills in a natural classroom environment created a gap in the current research literature.
Included in this chapter is the background of the study that describes word problem-solving skills students need to develop mathematics proficiency. Also included is an explanation of the requirements of IDEA (2004) and the ESSA (2015) policies that support schools use of the MTSS-RTI model to address the needs of all students with academic issues. Additionally, the next section described the MTSS-RTI tier two intervention followed by the problem statement, the purpose of the study, the research questions, and the conceptual framework. The chapter also included the nature of the study, definitions, assumption, Scope and delimitations, limitations, significance, and summary.
Children from different linguistic and cultural backgrounds, with and without disabilities struggle with developing mathematics word problem-solving strategies. Word problem-solving requires students to have reading comprehension skills and knowledge of mathematics concepts, procedures, and operations. Solving word problem demands that students can read, decode and understand the vocabulary, recognize the problem structure, extract relevant information, and select and apply the appropriate arithmetic algorithm (Wilson, 2013; Zheng, Flynn, & Swanson, 2013). Additionally, word problem-solving methods also require students to convert the information into arithmetical
equations, graphics or symbols and use a detailed solution strategy to solve it. The complexity of the stages and procedures in solving math word problems could be
challenging for most students. Students with language deficits, learning disabilities, low-performance and lack critical prerequisite math skills experienced challenges in
Teachers need to know and understand the problems students encounter in the general education classroom if they lack the prerequisite skills for mathematics word problem-solving and have other learning deficits. An understanding of the characteristics displayed by students with significant difficulties in solving word problems can help educators plan and implement appropriate interventions (Bryant et al., 2014). Griffin, League, Griffin, and Bae (2013) explained that children have problems developing accuracy and automatic retrieval of mathematics facts to choose and apply appropriate procedural strategies. Additionally, Powell, Fuchs, and Fuchs (2013) explained that learners do not understand the basic number combination which is crucial for developing other mathematical skills such as computations. Children with math word problem-solving difficulties have many learning deficits which included understanding the language of the problem, and not recognizing irrelevant information. The students also lack the skills to apply multiple steps; and experiencing difficulties in choosing and using the appropriate algorithms to solve the problem (Pfannenstiel, Bryant, Bryant, &
Porterfield, 2015).
According to Boonen, Koning, Jolles, and van der Schoot (2016), children have difficulties solving complex word problems, because they lack reading comprehension skills that help students identify and interpret the meaning of the vocabulary, phrase, sentence, and language within the word problem statement. Additionally, De Kock and Harskamp (2014) explained that students need skills to read, analyze a problem, determine the type of problem, develop an equation, solve the problem, and verify the answer. Additionally, teachers must have a comprehensive knowledge of the word
problem-solving processes, and prerequisite skills, as well as how the lack of prerequisite skills is revealed in students’ work.
Moreover, students may fail to attain mathematics proficiency because of insufficient opportunities to develop reasoning skills, concepts, and word problem-solving skills. Students might also have difficulties making useful connections with previous mathematics knowledge to understand new concepts in real-world situations (Doabler et al., 2014). Additionally, Jitendra et al., (2015) explained that children struggling to solve word problems display poor metacognitive and cognitive skills, deficiencies in language, concentration and working memory deficits that affect their learning. Similarly, Van Garderen, Thomas, Stormont, and Lemnke (2013) stated that learners have deficiencies in their prior knowledge, lack confidence in their mathematics skills. They also have language deficits, attention issues, impulsivity, memory
difficulties, and motivation problems. Teachers must put structures for instruction in place and provide appropriate opportunities for students to acquire skills in solving word problems, to build a solid foundation for future learning.
The aim of teaching mathematics in schools is to develop children’s practical knowledge, word problem-solving and application skills for employment, higher
education and functioning in society (Ernest, 2015; Nurlu, 2015). Children must be able to use mathematics to solve practical, real-world problems. Teachers must provide them with the foundational understanding and competencies needed to build further specialist knowledge and skills, which they can use beyond school (Ernest, 2015). Therefore, teachers use the MTSS-RTI to provide early identification, prevention, and intervention
for children in the classroom (Averill, Baker, & Rinaldi, 2014). The absence of well-structured instruction and intervention might be the reason for students’ failure to achieve mathematics proficiency. The IDEA (2004) and ESSA (2015) require that highly
qualified general and special education teachers provide all school-aged children with scientific research-based curricula, instruction, multi-tiered response to intervention tier two intervention, and assessment (King Thorius, Maxcy, Macy, & Cox, 2014). In the general education classrooms, there may be students with disabilities, students from the low socioeconomic background, English learners, African Americans, Native Americans, Asian, Hispanic and blended heritage children and White children (Averill et al., 2014). The IDEA (2004) and ESSA (2015) further require teachers to assess students
continuously during their instruction and intervention to monitor students’ progress (King Thorius et al., 2014; United States Department of Education, 2007). The aim is to give teachers a framework to provide all students with instructional opportunities to master mathematics knowledge, concepts, and skills.
Multi-Tiered Response to Intervention
The MTSS-RTI tier two intervention provides students who are having difficulties with the core mathematics instruction in the general education classroom with
intervention to diminish their deficits. Hunt, Valentine, Bryant, Pfannenstiel, and Bryant (2016) determined that MTSS-RTI tier two level instruction should be explicit,
systematic, and aligned with the mathematics core curriculum content. Hunt et al. (2016) suggested that schools develop a learning environment that supports building children’s mathematical foundation skills, procedures, concepts, and word problem-solving skills.
The tier two intervention should also include the scaffolding of learning, problem-solving strategies, provision of purposefully constructed evaluations and feedback. Bryant et al. (2014) also suggested that teachers pace instruction and provide multiple opportunities for students to participate in their learning. The evidence-based intervention should address the specific needs of the individual student.
The MTSS-RTI tier two intervention should address the task, with monitoring assessment, student practice items, and mastery benchmark. Teachers should model the new concepts and skills; provide guided and independent practice, and corrective feedback, with frequent review of the content during the period of instruction
(Valenzuela et al., 2014). Similarly, Jitendra et al. (2015) reviewed past studies and found that explicit strategy instruction was very efficient in helping children learn and
remember problem-solving strategies and skills. They explained that effective
mathematics interventions combine various cognitive and metacognitive instructional procedures resulting in positive effects on students’ learning. Students must be taught to monitor their thinking, question their answers to the problem, and review the process. Teachers’ pedagogical practices are essential in determining whether students are making adequate progress or have an innate disability.
Education policies make provisions for states and districts to utilize the MTSS-RTI model as one of the methods to promote whole-school interventions for subgroups of children with persistent academic underachievement (United States Department of
Education, 2007). The goals of the MTSS-RTI framework are to ensure the success of all learners and decrease the achievement gap between minorities and White students.
Minorities refer to students with disabilities, students from the low socioeconomic background, English language learners, African Americans, Native Americans, Asians, Hispanics and blended heritage children (Averill et al., 2014; United States Department of Education, 2007); Hughes & Brady, 2015). The fundamental principle of the MTSS-RTI model is all students can learn with the appropriate instruction and assessment monitoring structures (Brown, 2016).
The MTSS-RTI model is a systematic method, utilizing the analysis of student data to identify, define, and resolve students’ academic difficulties and behavior issues (Meyer & Behar-Horenstein, 2015). The findings of the qualitative case study revealed the structure and contents of the mathematics curriculum, the intervention program, and assessment tools fourth-grade teachers used to address students’ word problem-solving deficits. The research findings focused on how the teachers used scientific-based curricula, instruction, MTSS-RTI tier two intervention and assessment, and the analysis and interpretation of student data to decrease students’ math word problem-solving difficulties. The study findings described teachers’ perception of the effectiveness of the instruction, the intervention program, and assessment tools used for monitoring student progress in the classroom and intervention groups. The study findings also revealed the teachers’ perception of the effectiveness of the MTSS-RTI tier two intervention they used to address students’ difficulties in solving math word problems.
Problem Statement
Although many states and school districts have been implementing the MTSS-RTI as one of the whole-school strategies to address the academic difficulties of students;
many fourth-graders are failing to achieve proficiency in the core mathematics curriculum content (Kingsdorf & Krawec, 2014). The National Assessment of
Educational Progress (NAEP) (2015), the National Report Card showed that only 40% of the fourth-graders assessed in mathematics achieved proficiency. The NAEP report indicated that 19% of Blacks, 36% of Hispanics and 16% of students with disabilities achieved mathematics proficiency. This qualitative case study originated in Florida, where 39% of fourth-graders attained mathematics proficiency, according to the NAEP report. Table 1 indicates how MAC Elementary School (pseudonym) fourth-graders performed on the 2018 Florida Standards Assessments.
Table 1
Fourth-Graders Performance Levels on 2018 State Assessment
________________________________________________________________________ Number Percentage in Each Achievement Level___ Grade of Level 1 Level 2 Level 3 Level 4 Level 5 Students Inadequate Below Satisfactory Proficient Mastery Satisfactory
________________________________________________________________________ 4 143 41 18 24 11 6
Table I is a record of the results of the 143 fourth-graders who participated in the 2018 Florida Standards Assessments. Of the 143 students, 58 or (41%) students
performed at level 3 or above the Satisfactory level, while 85 (59%) students failed to reach Satisfactory. The students needed a MTSS-RTI tier two intervention to improve
their mathematics performance (Florida Department of Education, 2018). The school-based leadership team (SBLT) determine the placement and instruction for the 85 (59%) students who performed below the benchmark. Gonzales and Krawec (2014) stated that there are significantly more word problem-solving items in state assessments (e. g. Florida Standards Assessments) and national assessments (e. g. National Assessment of Educational Progress) than in the previous state and national assessments. Furthermore, Kingsdorf and Krawec (2014) specified that students’ performance on standardized achievement tests signified that students are having difficulties with the development of mathematical word problem-solving skills.
Faulkner and Cain (2013) attributed students’ failure to achieve mathematics proficiency to conditions within the school environment. Additionally, Wagner and Foote (2013) and De Kock and Harskamp (2014) indicated that teachers might lack the content and pedagogical knowledge needed to differentiate and teach math word problem-solving efficiently to diverse groups of students from different cultural and linguistic
backgrounds. The National Council of Teachers of Mathematics (2014) report indicated that many teachers have inadequate access to scientific, research-based instructional materials, assessment tools and the technology needed for instruction. Additionally, many teachers do not have the benefit of supportive structures and coaching, and mathematics professional development opportunities related to teaching and learning.
Ottmar, Konold, Berry, Grissmer, and Cameron (2013) explained that research findings revealed inequalities in mathematics education with regards to minority students’ exposure to diverse content. The authors discovered that year-after-year
elementary school teachers deprived minority students of opportunities to learn different and complex mathematics concepts. Ottmar et al. (2013) indicated that teachers who teach African American and Hispanic students focused on primary numbers and
operations, and computational skills with limited instruction in the other content strands and problem-solving.
The NAEP (2015) report and research findings indicated that there is a need for strategic intervention in fourth-grade classrooms to develop and strengthen the
mathematics skills of children with and without learning difficulties. The qualitative single-case study findings revealed how fourth-grade general and special education teachers’ practices in the regular classroom environment were similar or different from findings in the research literature.
Purpose of the Study
The purpose of this qualitative single-case study was to discover how fourth-grade special and general education teachers used the MTSS-RTI evidence-based instruction, intervention, assessment, and student data to teach math word problem-solving skills. The participants were five fourth-grade general and special education teachers charged with instructing children from diverse cultural and linguistic
backgrounds, with different abilities and disabilities. The study findings identified and described the strategies teachers employed in teaching mathematics concepts, procedures, skills instruction and intervention, and how teachers helped children develop strategies to solve real-world problems (Nurlu, 2015). The findings described the resources, socio-cultural, and pedagogical practices, teacher training, and support system in place for
fourth-grade teachers to implement the MTSS-RTI system. The findings explored the obstacles, challenges, and the successes the teachers experienced using the MTSS-RTI. The research revealed the roles and responsibilities of the special and general education teachers, and their perceptions of the MTSS-RTI model. The goal was to discover how the teachers utilized the MTSS-RTI components of evidence-based curricula and
intervention programs, differentiated instruction, and a comprehensive assessment system data to make instructional decisions.
Research Questions
An understanding of fourth-grade special and general education teachers’ perception of how they used the MTSS-RTI frameworks to teach math word problem-solving skills can help identify best teaching practices. The goal of the qualitative case study was to discover how fourth-grade teachers used MTSS-RTI practices to teach math word problem-solving to students using the following research questions.
• How do fourth-grade teachers use the MTSS-RTI for developing the mathematics
word problem-solving skills of children who have persistent and significant difficulties?
• What strategies do teachers adopt when teaching mathematics concepts,
procedures, and skills instruction and intervention to fourth-graders?
• How do teachers help fourth-grade children solve real-world problems and to
• What professional training, resources, support, and coaching has the district
school provided for teachers to implement the MTSS-RTI framework to address fourth-graders mathematics word problem-solving difficulties?
Conceptual and Theoretical Framework
Welner’s (2001) zone of mediation (ZOM) framework and Vygotsky’s (1978) sociocultural theory will be the conceptual and theoretical frameworks for this qualitative case study.
Vygotsky’s (1978) sociocultural theory illustrated how learners varied social and cultural backgrounds and experiences impacted and shaped children learning and how they interpreted and comprehended concepts. Vygotsky believed that an individual’s learning is a collaborative, social activity through which the individual created meaning because of his or her interactions with other people. Vygotsky’s Zone of Proximal Development (ZPD) described the ways participatory and social learning takes place. Teachers and peers who are more knowledgeable scaffold individuals learning of concepts and skills until they can work independently.
The ZPD assumed that students could produce their knowledge when teachers and peers provided them with guidance and meaningful, authentic learning experiences that replicated real-world situations and problems. The teacher’s role is to guide, assist, monitor, coach, facilitate learning, and inspire learners to take ownership of the learning process. In this study, the ZPD was used to illustrate how teachers utilized a small group and individual instruction and intervention to scaffold the learning of students who are having difficulties with math word problem-solving. Furthermore, the qualitative study
revealed the strategies teachers used to scaffold, facilitate and motivate student learning (Schreiber & Valle, 2013). This study provided evidence of how teachers scaffold student learning and help them develop their knowledge base, connect and organize new
information with their prior education and experiences.
Welner’s zone of mediation (ZOM) framework offers a way of highlighting the dynamic forces impacting the implementation of the policy to provide equal educational opportunities for all students. Policy implementation is a collaborative, social-cultural procedure that included teachers discussing, understanding and implementing the legislation. The sociocultural processes involved educators’ experiences, interpretations of the policy, the school’s administrative structure, cultural and teaching practices that influence implementing the MTSS-RTI framework (King Thorius et al., 2014; King Thorius & Maxcy, 2015).
Additionally, the conceptual approach focuses on educators’ interpretation of multi-tiered response to intervention procedures, processes, and practices, their subject knowledge, and pedagogical skills (King Thorius et al., 2014; King Thorius & Maxcy, 2015). The conceptual approaches also focused on how schools organized and managed staffing, training, and resources that are available for teachers’ participation in decision-making. Moreover, the ZOM illustrated the traditional and instructional practices in the school. In practice, ZOM comprised of the criterion used in assessing and grouping students for instruction. ZOM included inclusive practices, planning, instruction, staff collaboration and the delivery of services in general education classrooms. The ZOM
involved the schools’ arrangement for classroom instruction, general and special
educators co-teaching, planning, communication, conflict resolution, and collaboration. Furthermore, King Thorius and Maxcy (2015) explained that the ZOM influenced the strategies teachers used to determine students’ eligibility for intervention and special education. Subsequently, King Thorius et al. (2014) recommended that educators focus on the quality of the curriculum, teachers’ pedagogy and other environmental factors that can impact children’s learning, instead of focusing on deficits within the learner.
Additionally, the ZOM described the school operational functions and organizational capacities. School resources comprised of finances, assignment of teachers, curriculum and high-tech tools; curricular and co-curricular activities scheduling, professional development activities and student support services.
The ZOM was used in this study to illustrate how the elementary school’s administrative structure, cultural and pedagogical practices influence the MTSS-RTI framework implementation. Additionally, identifying the strategies teachers used to determine students’ eligibility for intervention. The ZOM also determined educators’ awareness of the beliefs, values, and cultural-linguistic practices of the children they teach, to provide appropriate instruction for all students and how teachers used the components of the MTSS-RTI to make educational decisions.
Nature of the Study
Merriam and Tisdell (2016) identified five qualitative approaches: a case study, ethnography, narrative inquiry, grounded theory, and phenomenology. After reviewing the quantitative, mixed methods, and the five qualitative research methods for this study,
the case study approach within the qualitative framework was selected. The narrative approach focused on the individual life story and was not appropriate to this study that focuses on how teachers used the MTSS-RTI practices to teach math word problem-solving (Merriam & Tisdell, 2016). Merriam and Tisdell (2016) indicated that a
phenomenological approach was better suited to studying human affective, emotional and often intense experience. The phenomenological approach was not suited to this study that focuses on teachers’ pedagogical practices with fourth-graders. An ethnographic approach was inappropriate because this research focused on the description of a specific culture, behaviors, social events, and institutions over time. The grounded theory was also considered and found to be inappropriate as the intention was not to develop a theory from the opinions, actions, and interactions of the participants (Merriam & Tisdell, 2016). Therefore, the qualitative single-case study was selected to discover how teachers used the MTSS-RTI tier two intervention to develop the mathematics word problem-solving skills of fourth-graders with significant learning difficulties.
Yin (2014) defined a case study as “an empirical inquiry that investigates a contemporary phenomenon (the “case”) in depth and within its real-world context especially when the boundaries between phenomenon and context may not be…evident” (p.16). Merriam and Tisdell (2016) explained that a case could be a phenomenon, a group, a single person, an institution, a community or specific policy. The case in this study is the fourth-grade special and general education teachers using the MTSS-RTI model to teach math word problem-solving to students with math difficulties. The
special and general education teachers used the response to intervention universal screening, intervention, and progress monitoring system to remediate students’
mathematics word problem-solving difficulties. Additionally, the case study approach provided an understanding of the use of the MTSS-RTI model within the complex social setting of the general education classrooms with students from diverse background and with different abilities or disabilities. It also described the school’s socio-cultural environment, teacher training, student assessment, data collection, analysis, interpretation, and decision-making system in place for fourth-grade teachers to implement the MTSS-RTI.
A variety of sources of evidence (example: interviews, observation, documents, and artifacts) is used in the qualitative single-case study approach to ensure the validity of the findings through triangulation of the data (Yin, 2014). Interviews, the teachers’ unit, and lesson plans, intervention programs, district training document, teachers’ guides, and assessment tools were the sources of data for this study. In-depth, open-ended interviews with five general and special education teachers provided the evidence in answer to the research questions.
The NVivo computer software program was used to managed, organized, and coded the interview transcripts, teachers’ unit, and lesson plans, intervention program, district training document, teachers’ guides, observation notes, and assessment tools. I entered each transcript into the latest version of NVivo computer software program for the final coding, analysis, and interpretation of the data. The interviewees’ exact words
and information from the district and professional development documents were included in the writeup of the research findings.
Definitions
Diagnostic assessment – testing to determine students’ strengths and weaknesses in a subject area topic. Teachers use diagnostic tests to identify the specific skill a student lack or is having difficulties with to prepare an appropriate intervention to remediate the problem (Danielson & Rosenquist, 2014).
Formative assessment - testing to determine students’ mastery of the skill or concept taught in a lesson. After explaining the skill or concept to the children, a test is given to determine if the student has mastered the skill or concept or need further instruction or practice (Jitendra, Dupuis, et al., 2014).
Inclusion - Students irrespective of ability, disability or language skills are educated together in the general education classroom. All students in the general education classroom participate in the curricula and co-curricular activities, screening, intervention, and assessment. (DeMatthews, 2015).
Intervention – instruction or training is given to a small group or individual students to remediate skills deficits for students with academic and behavioral difficulties. Students with problems in mathematics word problem-solving skills are assessed to identify the area of need. The teacher develops a plan for instruction to remediate their problems (Powell et al., 2013).
Math word problem – a mathematical exercise or story in which meaningful contextual information on the math topic is in the text. It is a combination of language
and numbers in which children apply math computation, cognitive and metacognitive processes to solve a problem (Orosco, 2014).
Professional development – is in-service knowledge and pedagogical skills training for educators. Through professional development, educators keep abreast of the changes in education policy, teaching strategies and curriculum content (Bocala, 2015).
Progress Monitoring – is frequent testing of students to gather information about their deficits and mastery of a targeted skill or concept, and the suitability or efficacy of the intervention. The result of the progress monitoring test is used to determine if the student needs more instruction or practice or do not need further guidance (Danielson & Rosenquist, 2014).
Response to Intervention – A multi-tier instruction delivery system that
incorporates a combination of whole-class evidence-based education and supplemental small-group intervention, and assessment for academically struggling students. All Students are screened three times during the school year. Students who failed to meet the benchmark received small group tier two intervention, and their progress monitored. Students who fail to make adequate progress by the second screening received tier three individual intervention and their progress monitored (Danielson & Rosenquist, 2014).
Research-based, or scientific-based instructions – are an accumulation of research on how children learn and how teachers must teach to ensure student achievement. The curriculum and instruction developed by researchers are then explained to educators during profession development undertakings (Averill et al., 2014).
Universal screening – testing administered multiple times during the school year to all children to identify children who achieved proficiency and those at-risk for
academic failure. The tests are curriculum based and cover the content and skills student should have at that specific time in the school year (Powell et al., 2013).
Assumptions
The assumptions explained aspects of the study that are believed but cannot be demonstrated to be true. Included are those assumptions that are relevant to this study (Walden University, 2012). One premise of this qualitative case study was the targeted school implements the MTSS-RTI with fidelity to ensure all students from different backgrounds with and without disabilities receive an evidence-based math education and intervention when they need it. Another assumption was the school has a functioning school-based MTSS-RTI team that implemented the MTSS-RTI principles, provided the training for teachers, scheduling, and resources. Also, fourth-grade special and general education teachers are following the CCSS-M and used evidence-based instructional materials and assessment tools to teach math word problem-solving skills. Another assumption was the school provides teachers with the instructional materials, tools, technology, and professional development opportunities related to the MTSS-RTI model and teaching and learning math. These assumptions were the focal point for discovering how fourth-grade special and general education teachers used the MTSS-RTI practices to provide tiered intervention to students with math word problem-solving difficulties.
Scope and Delimitations
The delimitations define the boundaries of the study by identifying the population, and the theories and conceptual frameworks related to the area of research that was investigated (Walden University, 2012). The evidence-based common core state standard in mathematics and the MTSS-RTI are an essential part of instruction in the elementary schools, yet 60% of fourth-grade students are failing to achieve proficiency in
mathematics (NAEP, 2015). There are significantly more word problem-solving items in the Florida Standards Assessment and the NAEP than in previous year’s state and
national assessments (Kingsdorf & Krawec, 2014). The state and school districts require schools to implement the MTSS-RTI screening, tiered intervention, and progress
monitoring system to provide instructions to students who are experiencing math word problem-solving difficulties. Math word problem-solving skills are essential for developing math proficiency. It is important to discover why fourth-grade students are failing to achieve math proficiency. Also, whether fourth-graders are receiving the kind of intervention and instruction with the appropriate material and assessments to achieve math proficiency. It is also essential to find out if the teachers have the knowledge and teaching skills they need to teach math word problem-solving.
Five fourth-grade special and general education teachers in an elementary school provided information about the use of the MTSS-RTI model for teaching math word problem-solving in the general education classrooms. Interviewing fourth-grade special and general education teachers provided the opportunity to discover teachers’
knowledge and skills to teach math word problem-solving. Interviews, teachers’ lesson plans, intervention programs, observation of tier two intervention, district training
document, and teachers’ guides and assessment tools were the sources for the inquiry and the results of the research questions. The research focused on how five fourth-grade special and general education teachers used the MTSS-RTI mathematics materials, and assessment tools available to them to address students’ math word problem-solving difficulties. The research findings may be generalized, in the districts and the schools with similar populations in the state.
Limitations
There are a few limitations to this study. The study focused on how five MAC Elementary School fourth-grade special and general education teachers used MTSS-RTI to teach math word problem-solving to students from different backgrounds with and without disabilities. The school established five years ago, received a D grade in the 2017-2018 school year. The research findings may not be generalized, in states, districts, and schools that do not have similar populations. To address this issue a detailed
description of contextual information about the school; a detailed description of the fourth-grade population, teacher qualification, training, and beliefs, how the student data is collected, analyzed and interpreted was included so readers can determine the extent to which the findings are transferable (Merriam & Tisdell, 2014). All efforts were made to research how the teachers used the MTSS-RTI to teach math word problem-solving with fidelity and without bias because of a genuine interest in discovering how teachers achieve their goals.
Significance
The qualitative case study findings were used to document and describe how the special and general education teachers used the MTSS-RTI instructional delivery system tier two intervention to remedy deficits and develop fourth-graders mathematical word problem-solving skills. The study findings also documented the kind of structure, training, and support systems that are in place for teachers to utilize the MTSS-RTI model to diminish the math word problem-solving deficits of fourth-graders with significant math difficulties. The study findings described the challenges, obstacles, and successes fourth-grade teachers experienced as they used the MTSS-RTI practices to teach math word problem-solving.
Schools serve minorities, English language learners, students with disabilities, and children from the low socioeconomic background, who are experiencing word problem-solving difficulties. The MTSS-RTI model ensured that teachers provide equal and first-class education opportunities to all students, with appropriate research-based instruction and intervention for children with learning problems (King Thorius et al., 2014). The study findings added to the literature showing the implementation of MTSS-RTI processes by general and special education teachers in the authentic classroom
environment to teach math word problem-solving to students with learning difficulties.
Social Change
The research findings provided a better understanding and appreciation of the MTSS-RTI screening, intervention, and progress monitoring assessments used in
effectiveness of their training, the use of MTSS-RTI instruction, intervention, assessments, data analysis, decision-making and time management. Through the interview process, teachers reflected on their classroom practices and determined what was needed to improve instruction, intervention, and assessment for students with learning difficulties in their math classes. Teachers gave learners with learning
difficulties more opportunities to learn complicated math word problem-solving concepts and develop and practice these skills. General and special education teachers worked collaboratively to develop a learning environment that supports building children’s math foundation and procedural skills, concepts and word problem-solving skills. The study findings added to the MTSS-RTI framework and mathematics research. The study findings provided readers with an in-depth account of how fourth-grade special and general education teachers interpreted and used the MTSS-RTI tier two intervention to decrease students’ mathematics word problem-solving difficulties.
Summary
The chapter described the research problem and purpose of the study, implementing the policy, MTSS-RTI to develop fourth-graders mathematics word problem-solving skills. The chapter also included a summary of recent research that impacted how teachers used MTSS-RTI procedures, practices, and processes in providing math word problem instruction and intervention. Also, added was the Welner’s zone of mediation (ZOM) used to describe the infrastructure, administrative structure, resources, and practices that should be in place for the effective implementation of the MTSS-RTI framework. Vygotsky’s sociocultural theory described the utilization of the MTSS-RTI
delivery system to develop fourth-graders skills in applying math knowledge to solve word problems. Also, included were the study’s background, problem statement, the purpose, research questions, and nature of the research, conceptual framework, definitions, limitations, the significance, ethical concerns, and summary.
Chapter 2 covers the review of literature which provided the conceptual
framework used to analyze and interpret the research findings of this study. The research was used to examine the use of the MTSS-RTI instruction delivery system to develop the mathematics word problem-solving skills of fourth-graders. The literature review
provided informed data-driven decision-making practices that formed the foundation for the study. The literature was sourced from Walden University’s library databases, government and professional websites. The information collected covered a range of topics such as math education, math difficulties, the CCSS-M, MTSS-RTI practices and the organization theory supporting MTSS-RTI.
Chapter 3 presented the research design and methodology. Included is a
description of the district and elementary school population; the criterion used to select participants for the study, ethical concerns, and methods of collecting, analyzing data and addressing bias in the study. All research methods were explored, and the qualitative case study was determined to be the most appropriate to answer the research questions.
In Chapter 4, I wrote the summary of the findings from interviews, teachers’ units, and lesson plans, intervention programs, district training document, and teachers’ guides and assessment tools that were the sources for the inquiry and answers to the research questions.
In Chapter 5, I discussed the results of the research based on the literature and conceptual framework, made recommendations and write the conclusion.
Chapter 2
Introduction
The mathematics curriculum is highly procedural, organized in strands, and adds different components across, and within each grade level. It continually builds on the previous knowledge and skills for successful learning. Thus, deficits in word problem-solving not remediated in the early grades can have lasting effects on future learning (Doabler et al., 2014; Kanive, Nelson, Burns, & Yesseldyke, 2014). Additionally, solving word problems is critical to helping students apply mathematics concepts and procedures to resolve real-world issues (Nurlu, 2015). Solving math word problems is an essential component of mathematics competency and the most challenging section for learners with difficulties (Driver & Powell, 2016; Jitendra, 2013; Jitendra et al., 2015, Krawec, 2014; Powell et al., 2013). Also, teaching mathematical word problem-solving to learners from different backgrounds, with and without disabilities can be very challenging for teachers who lack relevant mathematics knowledge and pedagogy skills (Van Garderen et al., 2013).
In the United States, many fourth-graders have difficulties solving math word problems. Students’ performance on standardized achievement tests reflected their difficulties with the development of mathematical word problem-solving skills
(Kingsdorf & Krawec, 2014). The National Assessment of Educational Progress (NAEP) (2015), National Report Card indicated that overall 60% of the fourth-graders assessed in mathematics did not achieve proficiency. The NAEP report indicated that 81% of Blacks, and 64% of Hispanics, and 84% of students with disabilities did not achieve mathematics
proficiency. The case study originated in a southern state, where 61% of fourth-graders did not achieve mathematics proficiency. It was important to discover how the targeted school is remedying students’ mathematics deficiencies. The study findings revealed how fourth-grade special and general education teachers used the MTSS-RTI instruction to address the math word problem-solving deficits of students from the diverse cultural and linguistic background, with different abilities and disabilities.
The students with mathematics difficulties have problems comprehending and solving simple one-step and complex multi-step word problem (Jitendra et al., 2015). Students with problems in the math word problem-solving exhibit a lack of deciphering and reading comprehension skills, poor vocabulary growth and attention to details and limited organizational skills. Furthermore, the students struggle with mathematics calculation, writing, planning, organizing and implementing the plan to solve the word problem (Wilson, 2013). Also, Gonsalves & Krawec, (2014) stated that in the era of CCSS-M, there are significantly more word problem-solving items in state assessments (e.g., Florida Standards Assessments) and national assessments (e.g., National
Assessment of Educational Progress) than in the previous state and national assessments. Additionally, of the eight CCSS-M, six are explicitly linked to word problem-solving (Kingsdorf & Krawec, 2014).
Faulkner and Cain (2013, and King Thorius et al., (2014) attributed students’ failure to achieve mathematics proficiency to conditions within the school environment. Additionally, Wagner and Foote (2013) submitted that students fail to reach proficiency because teachers have limited mathematics content knowledge and pedagogy skills which
are crucial to educating children from diverse backgrounds. Moreover, De Kock and Harskamp (2014) implied that teachers might lack the content and pedagogical
knowledge needed to differentiate, modify and teach word problem solving effectively to diverse groups of students. Furthermore, De Kock and Harskamp explained that teachers must teach students reading skills, how to analyze the problem, determine the type of problem, develop an equation, solve the problem, then verify the answer. Teachers need to know the mathematics curriculum and assessment, math instructional strategies, and knowledge of how students learn mathematics.
Teachers' knowledge of math content and pedagogy influenced children learning (McGee, Polly, & Wang 2013; Polly, Neale, & Pugalee, 2014). De Kock and Harskamp (2014), and Van Garderen et al. (2013) suggested that teachers' might not have the math content knowledge and MTSS-RTI practices to teach word problem-solving in inclusive classrooms. The authors suggested that teachers have a limited understanding of teaching and learning mathematics, which may result in an overemphasis on teaching techniques, low-level skills and reduced use of resources. According to Battey and Franke (2015) research findings, some educators in urban schools believe that African-American, Hispanic, low-income learners and girls do not have the innate abilities to learn
mathematics. Therefore, those teachers did not see the need to use different instructional techniques to provide the children with high-quality instruction.
Several researchers (King Thorius & Maxcy, 2015; Marsh & Farrell, 2015; Regan et al., 2015; Werts, Carpenter & Fewell, 2014) indicated that teachers complained about their lack of training for teaching students with diverse abilities and disabilities in the
classroom. Those teachers the researchers interviewed had difficulties implementing the MTSS-RTI system, evidence-based curriculum, and using pedagogical practices to ensure the improvement of student outcomes. Werts et al. (2014) stated that teachers complained about their lack of skills in interpreting students’ assessment results, analyze the data and using the findings to make instructional decisions. Teachers had difficulties coping with the new additional responsibilities in implementing multi-tiered response to intervention practices. The study findings revealed the type of training teachers received to improve their mathematics content knowledge and pedagogical skills, the multi-tiered response to intervention, instruction methods, data analysis, and decision-making. The study findings also detailed teachers’ perceptions of their training, use of the multi-tiered response to intervention, curriculum, intervention, assessments, data analysis, decision-making and time management.
Mathematics education reform emphasized excellence and equity education for all students (Van Garderen et al., 2013). Therefore, states use them as a blueprint for
mathematical instruction and practices for grades K-12 learners with and without difficulties in general education classrooms to thrive in school and prepare for college, career, and life (Common Core State Standards for Mathematics, 2014; Powell et al., 2013). The goals of the CCSS-M are to give all students a strong mathematics
foundation, including an understanding of concepts, procedural skill and fluency, and the capability to apply them to solving word problems. The fourth-grade standards provide guidelines for the mathematics concepts, procedures, and multi-step word problem-solving skills that student needs to acquire (Common Core State Standards for
Mathematics, 2014; Powell et al., 2013). The CCSS-M contains broad statements of the knowledge and skills learners are to achieve at each grade level. The mathematics standards do not include pedagogical guidance and instructional practices. Therefore, educators must deconstruct the state standards, differentiate instruction and improve assessment practices. Many states deconstructed the mathematics standards for teachers, providing teaching goals and student learning objectives. The learning goals and
objectives are lesson guides for developing appropriate instructional activities, aligning assessment systems for monitoring student progress, and communicating the data to other stakeholders (Konrad et al., 2014). Through CCSS-M, teachers shifted from the
assessment of learning to assessment for learning. Teachers implemented instructional practices and integrated formative and diagnostic assessment practices into the
preparation and delivery of instruction (California Department of Education, 2015). According to the IDEA (2004) and ESSA (2015), school districts and schools have to use a multi-tiered instructional delivery model to provide quality, evidence-based education for every child and intervention for learners with academic struggles. MTSS-RTI is a whole school multi-tiered model that incorporates whole-class differentiated instruction combined with small-group and individual intervention. The components of the MTSS-RTI model are universal screening, continuous progress monitoring, high-quality core instruction, and evidence-based tiered interventions. Three times during the school year, educators assess all students (universal screening) to detect math proficiency and mathematics deficits. Teachers pinpoint the skills in which students who failed to reach the benchmark are deficient and provide the MTSS-RTI tier two supplementary
evidence-based intervention. Students who have not mastered skills in MTSS-RTI tier two intervention received an individual tier three intervention (Meyer &
Behar-Horenstein, 2015; Regan, Berkeley, Hughes, & Brady, 2015; Sisco-Taylor, 2014). During the MTSS-RTI tier two and tier three interventions, teachers assess students' performance to monitor their progress, determine mastery, or decide who should continue with small-group instruction, or who need more intensive individual intervention (Meyer & Behar-Horenstein, 2015; Sisco-Taylor, 2014).
The qualitative single-case study approach was used to investigate how teachers used the MTSS-RTI model tier two intervention to develop fourth-graders with
significant mathematics difficulties, word problem-solving concepts, procedures, and skills. The study findings described the infrastructure, socio-cultural, and pedagogical practices, teacher training, school’s decision-making support system and explored the obstacles, challenges, and the successes educators experienced (Harlacher, Potter, & Weber, 2014).
This chapter of the research included the following topics: the conceptual and theoretical frameworks, mathematical word problem-solving instruction, mathematical word problem-solving difficulties, MTSS-RTI model delivery system, and implementing the MTSS-RTI model. The chapter also included MTSS-RTI strategies, challenges, and benefits of MTSS-RTI implementation, roles, and responsibilities of educators
co-teaching and the multi-tiered response to intervention process, professional development, gaps in the literature, and summary.